**1 Review of Numerical Computation.**

1-1 The Real Numbers.

1-2 Addition and Subtraction.

1-3 Multiplication.

1-4 Division.

1-5 Powers and Roots.

1-6 Combined Operations.

1-7 Scientific Notation and Engineering Notation.

1-8 Units of Measurement.

1-9 Percentage.

Chapter 1 Review Problems.

**2 Introduction to Algebra.**

2-1 Algebraic Expressions.

2-2 Adding and Subtracting.

Polynomials 59 2-3 Laws of Exponents.

2-4 Product of Two Monomials.

2-5 Product of a Multinomial and a Monomial.

2-6 Product of Two Binomials.

2-7 Product of Two Multinomials.

2-8 Powers of Multinomials.

2-9 Removing Symbols of Grouping.

2-10 Quotient of Two Monomials.

2-11 Dividing a Polynomial by a Monomial.

2-12 Quotient of Two Polynomials.

Chapter 2 Review Problems.

**3 Simple Equations and Word Problems.**

3-1 Solving First-Degree Equations.

3-2 Solving Word Problems.

3-3 Uniform Motion.

3-4 Financial.

3-5 Mixtures.

3-6 Statics.

3-7 Work, Fluid Flow, and Energy Flow.

Chapter 3 Review Problems.

**Functions.**

4-1 Functions and Relations.

4-2 More on Functions.

Chapter 4 Review Problems.

**5 Graphs.**

5-1 Rectangular Coordinates.

5-2 Graphing an Equation.

5-3 Graphing a Function by Calculator.

5-4 The Straight Line.

5-5 Solving an Equation Graphically.

Chapter 5 Review Problems.

**6 Geometry.**

6-1 Straight Lines and Angles.

6-2 Triangles.

6-3 Quadrilaterals.

6-4 The Circle.

6-5 Volumes and Areas of Solids.

Chapter 6 Review Problems.

**7 Right Triangles and Vectors.**

7-1 The Trigonometric Functions.

7-2 Solution of Right Triangles.

7-3 Applications of the Right Triangle.

7-4 Introduction to Vectors.

7-5 Applications of Vectors.

Chapter 7 Review Problems.

**8 Oblique Triangles and Vectors.**

8-1 Trigonometric Functions of Any Angle.

8-2 Finding the Angle When the Trigonometric Function Is Kown.

8-3 Law of Sines.

8-4 Law of Cosines.

8-5 Applications.

8-6 Resultants of Nonperpendicular Vectors.

Chapter 8 Review Problems.

**9 Systems of Linear Equations.**

9-1 Systems of Two Linear Equations.

9-2 Other Systems of Equations.

9-3 Applications.

9-4 Systems of Three Linear Equations.

Chapter 9 Review Problems.

**10 Matrices and Determinants.**

10-1 Introduction to Matrices.

10-2 Solving Systems of Equations by the Unit Matrix Method.

10-3 Second-Order Determinants.

10-4 Higher-Order Determinants.

Chapter 10 Review Problems.

**11 Factoring and Fractions.**

11-1 Common Factors.

11-2 Difference of Two Squares.

11-3 Factoring Trinomials.

11-4 Other Factorable Expressions.

11-5 Simplification of Fractions.

11-6 Multiplication and Division of Fractions.

11-7 Addition and Subtraction of Fractions.

11-8 Complex Fractions.

11-9 Fractional Equations.

11-10 Literal Equations and Formulas.

Chapter 11 Review Problems.

**12 Quadratic Equations.**

12-1 Solving a Quadratic Equation by Calculator.

12-2 Solving a Quadratic by Formula.

12-3 Applications.

Chapter 12 Review Problems.

**13 Exponents and Radicals.**

13-1 Integral Exponents.

13-2 Simplification of Radicals.

13-3 Operations with Radicals.

13-4 Radical Equations.

Chapter 13 Review Problems.

**14 Radian Measure, Arc Length, and Rotation.**

14-1 Radian Measure.

14-2 Arc Length.

14-3 Uniform Circular Motion.

Chapter 14 Review Problems.

**15 Trigonometric, Parametric, and Polar Graphs.**

15-1 Graphing the Sine Wave by Calculator.

15-2 Manual Graphing of the Sine Wave.

15-3 The Sine Wave as a Function of Time.

15-4 Graphs of the Other Trigonometric Functions.

15-5 Graphing Parametric Equations.

15-6 Graphing in Polar Coordinates.

Chapter 15 Review Problems.

**16 Trigonometric Identities and Equations.**

16-1 Fundamental Identities.

16-2 Sum or Difference of Two Angles.

16-3 Functions of Double Angles and Half-Angles.

16-4 Evaluating Trigonometric Expressions.

16-5 Solving Trigonometric Equations.

Chapter 16 Review Problems.

**17 Ratio, Proportion, and Variation.**

17-1 Ratio and Proportion.

17-2 Similar Figures.

17-3 Direct Variation.

17-4 The Power Function.

17-5 Inverse Variation.

17-6 Functions of More Than One Variable.

Chapter 17 Review Problems.

**18 Exponential and Logarithmic Functions.**

18-1 The Exponential Function.

18-2 Logarithms.

18-3 Properties of Logarithms.

18-4 Exponential Equations.

18-5 Solving Logarithmic Equations.

Chapter 18 Review Problems.

**19 Complex Numbers.**

19-1 Complex Numbers in Rectangular Form.

19-2 Complex Numbers in Polar Form.

19-3 Complex Numbers on the Calculator.

19-4 Vector Operations Using Complex Numbers.

19-5 Alternating Current Applications.

Chapter 19 Review Problems.

**20 Sequences, Series, and the Binomial Theorem.**

20-1 Sequences and Series.

20-2 Arithmetic and Harmonic Progressions.

20-3 Geometric Progressions.

20-4 Infinite Geometric Progressions.

20-5 The Binomial Theorem.

Chapter 20 Review Problems.

**21 Introduction to Statistics and Probability.**

21-1 Definitions and Terminology.

21-2 Frequency Distributions.

21-3 Numerical Description of Data.

21-4 Introduction to Probability.

21-5 The Normal Curve.

21-6 Standard Errors.

21-7 Process Control.

21-8 Regression.

Chapter 21 Review Problems.

**22 Analytic Geometry.**

22-1 The Straight Line.

22-2 Equation of a Straight Line.

22-3 The Circle.

22-4 The Parabola.

22-5 The Ellipse.

22-6 The Hyperbola.

Chapter 22 Review Problems.

**23 Derivatives of Algebraic Functions.**

23-1 Limits.

23-2 Rate of Change and the Tangent.

23-3 The Derivative.

23-4 Rules for Derivatives.

23-5 Derivative of a Function Raised to a Power.

23-6 Derivatives of Products and Quotients.

23-7 Other Variables, Implicit Relations, and Differentials.

23-8 Higher-Order Derivatives.

Chapter 23 Review Problems.

**24 Graphical Applications of the Derivative.**

24-1 Equations of Tangents and Normals.

24-2 Maximum, Minimum, and Inflection Points.

24-3 Sketching, Verifying, and Interpreting Graphs.

Chapter 24 Review Problems.

**25 More Applications of the Derivative.**

25-1 Rate of Change.

25-2 Motion of a Point.

25-3 Related Rates.

25-4 Optimization.

Chapter 25 Review Problems.

**26 Integration.**

26-1 The Indefinite Integral.

26-2 Rules for Finding Integrals.

26-3 Simple Differential Equations.

26-4 The Definite Integral.

26-5 Approximate Area under a Curve.

26-6 Exact Area under a Curve.

Chapter 26 Review Problems.

**27 Applications of the Integral.**

27-1 Applications to Motion.

27-2 Applications to Eletric Circuits.

27-3 Finding Areas by Integration.

27-4 Volumes by Integration.

Chapter 27 Review Problems.

**28 More Applications of the Integral.**

28-1 Length of Arc.

28-2 Area of Surface of Revolution.

28-3 Centroids.

28-4 Fluid Pressure.

28-5 Work.

28-6 Moment of Inertia.

Chapter 28 Review Problems.

**29 Trigonometric, Logarithmic, and Exponential
Functions.**

29-1 Derivatives of the Sine and Cosine Functions.

29-2 Derivatives of the Other Trigonometric Functions.

29-3 Derivatives of the Inverse Trigonometric Functions.

29-4 Derivatives of Logarithmic Functions.

29-5 Derivatives of the Exponential Functions.

29-6 Integrals of the Exponential and Logarithmic Functions.

29-7 Integrals of the Trigonometric Functions.

29-8 Average and Root Mean Square Values.

Chapter 29 Review Problems.

**30 First-Order Differential Equations.**

30-1 Definitions.

30-2 Solving a DE by Calculator, Graphically, and Numerically.

30-3 First-Order DE: Variables Separable.

30-4 Exact First-Order DE.

30-5 First-Order Homogeneous DE.

30-6 First-Order Linear DE.

30-7 Geometric Applications of First-Order DE.

30-8 Exponential Growth and Decay.

30-9 Series RL and RC Circuits.

Chapter 30 Review Problems.

**31 Second-Order Differential Equations.**

31-1 Second-Order DE.

31-2 Constant Coefficients and Right Side Zero.

31-3 Right Side Not Zero.

31-4 Mechanical Vibrations.

31-5 RLC Circuits.

Chapter 31 Review Problems.

**Appendices.**

A Summary of Facts and Formulas A-1.

B Conversion Factors A-27.

C Table of Integrals.

D Answers to Selected Problems.

**Indexes.**

Index to Applications.

General Index.